Syntax: This is a complex sentence. 'You might've been hurt, babe' is the main clause using the present perfect tense ('have been hurt') with the modal verb 'might' to express possibility. 'That ain't no lie' is an informal tag clause affirming the truth of the previous statement. 'You've seen them all come and go' is a second independent clause using the present perfect tense ('have seen') to describe an experience with a result relevant to the present.
Morphology: 'might've' is a contraction of 'might have'. 'ain't' is a non-standard contraction often meaning 'am not', 'is not', 'are not', 'has not', or 'have not'. Here it means 'is not'. 'You've' is a contraction of 'you have'. The verbs 'been', 'seen', 'come', and 'go' are past participles used with the auxiliary 'have' to form the present perfect tense.

Syntax: 'I remember you told me' is the main clause with 'I' as subject, 'remember' as the main verb, and 'you told me' as the object clause. 'That it made you believe in no man, no cry' is a relative clause introduced by 'that', explaining what was told. 'It' refers to the past hurt mentioned earlier.
Morphology: 'told' is the simple past tense of 'tell'. 'made' is the simple past tense of 'make', functioning as a causative verb (it caused you to believe). 'believe' is a base form verb following the preposition 'in'.

Syntax: 'Every little thing I do' is the subject of the clause, with 'I do' as a relative clause modifying 'thing'. 'never seems enough for you' is the predicate. 'You don't want to lose it again' is a simple declarative sentence in the present simple tense, stating a current desire/fear. 'But I'm not like them' is a contrasting clause using the comparative structure 'not like'.
Morphology: 'seems' is the third person singular present tense of 'seem'. 'don't' is the contraction of 'do not'. 'lose' is the base form verb following 'to'. 'I'm' is the contraction of 'I am'. 'them' is the object pronoun referring to the previous partners.

Syntax: 'Baby, when you finally get to love somebody' is an adverbial clause of time introduced by 'when'. 'Guess what' is an informal interjection used to introduce surprising or significant information. 'It's gonna be me' is the main clause, with 'it' as a dummy subject referring to the unspecified 'somebody' from the previous clause, and 'gonna be' as the future construction.
Morphology: 'finally' is an adverb modifying the verb phrase 'get to love'. 'get to' is a phrasal verb meaning 'have the opportunity to'. 'gonna' is an informal contraction of 'going to', used to form the future tense. 'be' is the base form of the verb 'to be'.

Syntax: 'You've got no choice, babe' is a simple declarative sentence. 'But to move on' is an infinitive phrase showing the only alternative. 'And you know there ain't no time to waste' is a compound sentence joined by 'and', using the existential 'there' construction. 'Because you're just too blind to see' is a subordinate clause of reason. 'But in the end, you know it's gonna be me' is the main contrasting conclusion, with 'in the end' as a prepositional phrase acting as a temporal adverb.
Morphology: 've got' is an informal equivalent of 'have'. 'ain't no' is a double negative in informal English, here meaning 'is no'. 'to waste' is the infinitive form. 'you're' is a contraction of 'you are'. 'blind' is an adjective. 'to see' is the infinitive. 'gonna' is again the contraction for 'going to'.